I have to find a really bad example where you cannot apply Heaths Theorem because of a missing functional dependency.

But am I right, that every relation has at least one functional dependency?

Or can anyone of you come up with an example table with at least 3 Sets of Attributes to project it and then join it together. The result should of course be different from the original table to proof Heath's Theorem right (no FD -> no lossless decompositions)

It does not matter, wheter it is an sql example or an abstract one.

## Best Answer

Relation can has no functional dependencies, if it has no non-key attributes, i.e. it is full-keyed relation.